**reflexive**,

**symmetric**, and

**transitive**.

We have a set A and R is a relation on that set.

1. R is

**reflexive**on A if and only if for all x that is an element of A, x relates to x, or x R x.

2. R is

**symmetric**if and only if for all x and y in A the relation of x to y is the same as the relation of y to x.

3. R is

**transitive**if and only if for all x,y, and z that are elements in A, if x relates to y, and y relates to z, then x relates to z.

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